Rotation Definition and 1000 Threads

I am trying to both design a code for Arduino and build a circuit connected with the Arduino which uses 3 anode 7 segment and 3 resistor arrays with 7 pins to connect to the Arduino Uno. The encoder is a rotary encoder. I have Pin A of the rotary encoder connected to pin 13 of the Arduino and...

Homework Statement Four equal discs of mass ocuppy the vertices of a square frame made by four rigid bars of length and negligible mass. The frame is at rest on a horizontal table, and it can move with negligible friction. An instantaneous impulse is transmitted to one of the masses, in the...

An artillery shell is fired at, let's say, a 45 degree angle. The shell will rise to a maximun height and then fall back to earth, but the shell will also rotate considerably so that it strikes the ground with the nose forward. What accounts for the rotation? It would seem that the center of...

If I move a coordinate system by an angle theta, why does the vector still have the same direction, but the components are different?

Homework Statement Consider the Godel Metric in spherical coordinates as on page 6 here; ds^2=4a^2\left[-dt^2+dr^2+dz^2-(\sinh^{4}(r)-\sinh^{2}(r))d\phi^2+2\sqrt{2}\sinh^{2}(r)dt d\phi)\right] This is a solution to Einstein's Equations if we have ##a=\frac{1}{2\sqrt{2\pi\rho}}## and ##\Lambda...

A cube with mass M and length 2a, move in the velocity v on the friction-less horizontal table, when it closes to the end of the table, it is stopped by the long block(the height can be ignored), ask what is the value of v to topple from the table? ( note: use one side of cube as the rotating...

While resolving a problem in mechanics I discovered a beautiful and easy way for finding out what the rotation matrices in 3 dimensions are! And I'm surprised that I do not find this method anywhere on the internet! Would it be because it's not technically correct? Anyways, here it is: It's all...

If we have two frames related by ##x' = Rx## where ##R## is a rotation matrix and ##t'=t## Newton's law doesn't remain the same, for $$m \frac{d^2 x'}{dt'^2} = m \frac{d^2 Rx}{dt^2} = mRa$$ whereas it will be just ##ma## in the other frame. How do we solve this?

Homework Statement A horizontal platform rotates around a vertical axis at angular velocity ω. A disk with radius R can freely rotate and move up and down along a slippery vertical axle situated at distance d > R from the platform’s axis. The disk is pressed against the rotating platform due to...

Homework Statement A cylinder of mass M and radius R is resting on a horizontal platform (which is parallel to the x-y plane) with its axis along the y- axis and free to rotate about its axis. The platform is given a motion in the x-direction given by x= Acos(ωt). There is no slipping between...

for those Who Dont know golf. Swing weight is a measurment how Heavy the clubhead Feels. If i put on a heavier grip the swingweight falls. Heavier head swing weight goes up etc. If i Want to swing the Club with as little clubhead rotation as possible (i know forarm creats the rotation) Would i...

Homework Statement This is a practice olympiad problem A light rod with length l is hinged in such a way that the hinge folds in one plane only. The hinge is spun with angular speed ω around a vertical axis. A small ball is fixed to the other end of the rod. (a) Find the angular speeds for...

Spiral galaxies of course rotate around one axis perpendicular to the plane, but has anyone measured if any spiral galaxies are also rotating about an axis through the plane or about any other axis?

There's enough angular momentum in electron spin to get a 1cm radius ring of silver atoms to turn with a period of order days after relaxing from spin-up into randomness. (assuming you could get all of it to show up externally, and not end up in microscopic rotations or l quantum numbers.) I...

If I need 50,000 Nm of torque to rotate a wheel, and I am rotating it about its rim (like the London eye), would 5 10,000 Nm motors each connected to a set of tyres to rotate it (the motors are not connected to each other), or would these motors first need to be connected to each other and then...

Homework Statement A phonograph record is whiring around at 103 rpm. Two balls of mass 1 kg are sitting on the disk and are at rest with respect to disk. The first ball (1) sits at a radius 5 away from center. The second ball (2) sits at a radius of 10 away from center. What is the ratio of...

Good Day I have been having a hellish time connection Lie Algebra, Lie Groups, Differential Geometry, etc. But I am making a lot of progress. There is, however, one issue that continues to elude me. I often read how Lie developed Lie Groups to study symmetries of PDE's May I ask if someone...

Homework Statement Homework Equations ##\tau = rFsin(\theta)## ##\tau_{net} = I\alpha## ##F = -kx## ##kx = mg## The Attempt at a Solution I don't understand how the restoring force from the bending of the ruler behaves (so I have no idea how to apply torque here). I also don't understand how...

Homework Statement Hi good morning to all. The problem at hand states, that the points A (3,0) and B (5,0) are reflected in the mirror line y=x. Determine the images A' and B' of these points. I've done that using the reflection in the line y=x which i know to be \begin{bmatrix} 0 &1 \\ 1 & 0...

I'm trying to figure out whether it is best to use a multi-wheel or track system to get an object over a step, however I'm having a bit of trouble finding the torque needed for a track to pull itself up and over. Diagram of course is not to scale, but I've drawn up something of the situation...

Homework Statement A perfectly elastic spring swings in a vertical plane as a simple pendulum with a mass m suspended at the bottom of the spring. The force constant for this spring is ##k## and the unstretched length is ##L##. The spring is carefully held in the horizontal position so that the...

Homework Statement A perfectly solid marble of radius R rolls without slipping at the bottom of a spherical bowl of a radius 6R. The marble rolls back and forth in the vertical plane executing simple harmonic motion close to the lowest point. How long does it take the marble to go down one side...

Hi, Forgive me for this trivial question. I am confused. Let's say I have a gyroscopic device in which the rotor is set to spin at a prescribed angular velocity. Next, put it on an ocean surface in which the ocean waves induce a precession. These two rotations, then induce a moment (induce a...

In absence of any other forces, if you push a free object not on the center of mass, during the application of the force (not after) should it only rotate around its instantaneous center of rotation (also called pole or center of oscillation/percussion)? Or it can also be subjected to...

Homework Statement A pendulum having a bob of mass ##m## is hanging in a ship sailing along the equator from east to west. If the ship sails at speed v what is the tension in the string?. Angular speed of Earth's rotation is ## \omega ## and radius of the Earth is ## R ## Homework Equations...

Well, my physics teacher taught us about rotation the other day and I came across a scenario where a sphere and a ring roll down a friction-less inclined plane from a point of absolute rest. I found it counter-intuitive as I started to think about why would they start rolling in the first place...

My question is perhaps as much about the philosophy of math as it is about the specific tools of math: is perpendicularity and rotation integral and fundamental to the concept of multiplication - in all number spaces? As I understand it, the product of complex numbers x = (a, ib) and y = (c...

I studied statics but I thought I can figure out the dynamics part. In a rectangular shape that is tipping, Usually we take the center of mass as an axis of rotation however the center of mass is accelerating with centripetal force so taking it would make the problem complex and we just take...

Hi all! I'm currently working on a graphics/physics engine. The following Wikipedia page was extremely helpful in making rectilinear collisions look natural: https://en.wikipedia.org/wiki/Elastic_collision#Two-dimensional Specifically, the very general vector form of the equation on the bottom...

Issues about two topics were discussed in another thread. https://www.physicsforums.com/threads/do-solar-tides-affect-Earth's-orbit.933073/ The topics are: how do the lunar tides (1) cause the Earth's rotation to slow down, and (2) cause the moon to move away from the Earth. This thread is...

Homework Statement A circular disc of radius 25 cm and mass 0.5 kg is revolving in its plane with an angular velocity of 4 radians per second. Find A) its kinetic energy of rotation, and B) its new angular velocity if a mass of 10 kg is suddenly fixed on the rim of the disc. Homework...

Homework Statement There is a uniform rod of mass m = 1 kg and length L = 0.2 m fixed to the wall by an axis passing through its end. A uniform ball of mass M = 0.1 kg and radius R = 2.85 cm is on the ground, below the axis of the rod, such that the rod's unfixed end is at the height of the...

Homework Statement A uniform spherical shell rotates about a vertical axis on frictionless bearings. A light cord passes around the equator of the shell, over a light, frictionless pulley, and is attached to a small object that is otherwise free to fall under the influence of gravity. Calculate...

Just to confirm a few points: A body frame rotates with a body. It need not be aligned to the rotation axis. Angular momentum vector always aligned with rotation axis (not deviates from it). An observer on the body surface (body frame) observes no motion on a body. Principal axis of rotation...

Hi, me and a friend were discussing calendars and how they go wrong. Apparently one orbit around the sun happens during, on average, 365.242189 rotations around Earth's axis. The persian calendar almost nails it, with a 1 sec per year error, because it is based on star observations rather than...

Homework Statement I am referring to this thread and question: https://www.physicsforums.com/threads/rotation-of-a-spool-about-rough-ground.295666/ Here is the problem, restated: Homework Equations ##\tau_{net} = I\alpha## ##\tau = Frsin(\theta)## ##F_{net} = Ma_{cm}## ##\alpha = a_{cm} /...

As a student taking my first step into rotational physics in a classroom filled with students who have a year of this ahead of me I beg for help! :P So what is Rotational velocity? What does it define? How do signs work with rotation? What does its acceleration mean? Angular Velocity is...

Homework Statement In this diagram, I wondered if there is any torque due to the normal force from the hinge, once the support stick is removed. I also want to know what the normal force would be at the hinge. The cup and ball are to be ignored here (essentially massless). Homework Equations...

The planets rotate around our sun faster and faster the closer they are.The Suns rotate around a black hole in a galaxy as if they were a record on a record player.Gravitational laws as we understand them don't seem to apply.Is it possible that a black holes gravitational pull not only freezes...

Homework Statement The object is made out of multiple parts. The inertia matrices of every part are given. Only one part is rotating. How do I find the total inertia matrix. Homework EquationsThe Attempt at a Solution I thought that I could sum the inertia matrices, after tranforming them to...

Homework Statement I am studying for a test and am struggling with this question on the practice exam. The answer is 9.9 I am not sure how she got to the answer though A hoop of mass 300 g. and a radius of 20 cm rotates about an axle at the edge of a hoop. The hoop starts at highest...

Homework Statement The two blocks, m1 = 3.3 kg and m2 = 4.8, in the figure below are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.64 N · m. If the blocks...

Hi The first thing to say about this is that I don’t have a clue where to start. What I’m looking for is somewhere (maybe a website or just a brief introduction) I can study – and learn – about the forces involved and the maths required. _______ Say I have an item/length/beam/weight/etc (C...

Hi, The goal here is to increase/decrease the angle x by 5 degrees. the black circles represent a rubber tire (same as car tires, only smaller), 5cm in diameter, rotating on it's center, powered by a motor. each wheel has 40 psi (2.76 bar) of air in it. the yellow tray on both diagrams are...

Homework Statement 13.69 A packege of mass m is placed inside a drum that rotates in the vertical plane at the constant angular speed ##\dot {θ} = 1.36 rad/s##. If the package reaches the position θ = 45deg before slipping, determine the static coefficient of friction between the package and...

Homework Statement A thin, uniform, 18.5 kg post, 2.10 m long, is held vertically using a cable and is attached to a 5.00 kg mass and a pivot at its bottom end (as shown below). The string attached to the 5.00 kg mass passes over a massless, frictionless pulley and pulls perpendicular to the...

Homework Statement A solid cylinder rotates till it comes to rest. It has inititial angular velocity. To stop the drum a mass m ishung the belt which has a friction coefficient with the drum material as u we have to find no of rotationd all the data is known and correct Homework Equations...

How author derives these old basis unit vectors in terms of new basis vectors ? Please don't explain in two words. \hat{e}_x = cos(\varphi)\hat{e}'_x - sin(\varphi)\hat{e}'_y \hat{e}_y = sin(\varphi)\hat{e}'_x + cos(\varphi)\hat{e}'_y

Is there any physics approach useful to establish what should happen to a Newton's water bucketful rotating in a hypothetically empty universe (but for the bucket)? What the bucket would be rotating respect to in that one-bucket-universe? Everything rotating seems to have absolute (not relative)...

I apologize for the simple question, but I am trying to understand the Mass Discrepancy-Acceleration Relation and its relationship to ##\mu(x)## (from https://arxiv.org/pdf/astro-ph/0403610.pdf). The mass discrepancy, defined as the ratio of the gradients of the total to baryonic...